The problem here is that the mathematical models are not mechanical explanations. This is always glossed over entirely. Feynam was a genius because he was able to visualize and instead of dealing with long, difficult equations, he made pictures – the Feynman diagrams – to make the mathematics easier to do. It was a visual shortcut. In vector math, you can add vector arrows by putting one arrow on the end of another arrow, thus what was a difficult equation turns into a simple geometric diagram of arrows that is very intuitive.

The problem is that this is a model of the mathematics, NOT the physical mechanism at work in the world.

Finding a logarithm, you may recall, is the inverse action of raising some base number to an exponent. Which is to say that “finding the log” is to “find the exponent” that was raised on some base number.

log10 x = y (which is read as “y is the logarithm of x to base 10”).
The inverse of this statement is the exponential form, 10^y = x.

If we say “10^2 = 100”, then the inverse is “log10 100 = 2”.

Exponential functions and logs are all about how GROWTH relates to TIME. In these formulas, the “y” and the “2” are the time component. The “x” and the “100” are the growth component. Let’s look again:

log10 100 = y (how much TIME until 10 grows to 100?)
10^2 = x (how much GROWTH will 10 produce after 2 time units?)

Let’s take a shortcut from logs to natural logs, where the relationship to time is more direct because natural logs are based on the transcendental number e, which in turn, is about continuous growth. Natural log is referenced with the term “ln” and the natural log of 1 is zero.

ln(1)=0

Awesome. What does this mean? How much TIME until my investment grows to itself? Answer? Zero. My investment is itself already. Similarly, the formula, ln(2)=x is asking the question, “how long until my investment doubles?

Ok so what does ln(.5)=x mean?

We can calculate this, and interpret the calculation as meaning that to “grow” by half, you just need to go “backwards in time” for a while until your something has “grown” in half. Whatever that “while” turns out to be, equals x.

The point…

If our interpretation of log10 100 = y is how much time until 10 grows to 100, which is a valid interpretation, then we are forced to interpret ln(.5)=10 as meaning that we have to go backwards in time for 10 units to lose half our investment.

The math has no problem with this, but we do. Because it does not make sense in the real, actual world. The formula is valid, and useful. But we need a better interpretation.

This has happened many times in the history of mathematics. Our interpretations have had to change. Zero. Negative numbers. Irrational Numbers. Imaginary Numbers. Transcendental Numbers. Trans-infinite Numbers. Each of these caused a re-mapping in our brains of Number itself. Imaginary Numbers are the best example. These numbers can not represent any “thing” in our world like the number “3” can represent. And yet they are an extremely useful, and necessary number for solving all sorts of real world engineering and physics problems!

There was very real difficulty in explaining these numbers, interpreting them. Finally, in a turn of irony, we find a useful picture with Descartes’ own analytical geometry – the x and y coordinate system. Unitl the Imaginary numbers, we always visualized numbers as little dots on a “line”. In other words, we thought of Number in only one dimension. Descartes coined the term “imaginary number” as a derision against them, but it was his system that allows us to visualize these numbers properly: as two-dimensional numbers: literally, numbers that have “jumped off the line”. Thus there are so many more imaginary numbers than real numbers that the imaginary numbers make the real numbers look rather insignificant in comparison.

The lesson here is that these entities were derided and chastised and labeled “imaginary” at the time, simply because we lacked any interpretation that made sense with which to explain them to ourselves.

This is the current situation with Quantum Mechanics. It is in want of a better interpretation. The formulas work great. What they mean, we just don’t know. So we say that particles go backwards in time, simply because we have to say something. As far as the equations are concerned, this is “accurate”. But these equations are simply mathematical descriptions just like the log equation above. The equations of quantum mechanics do not describe any physical thing any more than the ln(.5)=10 describes the path my money takes through time to cut itself in half. They simply calculate where a particle is probably going to be. HOW it gets there is a total mystery. A TOTAL mystery.

Everyone misses this. But if you listen to Feynman, he is very clear about it. The physicists know this, deep down. They just allow the fallacy because it allows them to get on with their work.

The truth is that we have no explanation for what a photon is, what it looks like, or how it does what it does. We cannot explain this any more than we can explain what causes inertia gravity, or mass.

The most basic fundamental forces in the universe are still far beyond our comprehension.

“Ever the winds blow; ever the grass grows. Every day, men and women, conversing, beholding and beholden. The scholar is he of all men whom this spectacle most engages.”
Ralph Waldo Emerson, "The American Scholar"

The practice of Centering Prayer is basically a waiting upon God with loving attentiveness, fulfilling the Gospel injunction, “Watch and Pray.” If one can accept the notion of prayer as primarily relationship with God, it becomes obvious that one’s relationship with God can be expressed without words, simply by a gesture or even by one’s silent intention to consent to God’s presence.

"What amazed and upset him most of all was that the majority of people of his age and circle, who had replaced their former beliefs, as he had, with the same new beliefs as he had, did not see anything wrong with it and were perfectly calm and content. So that, besides the main question, Levin was tormented by other questions: Are these people sincere? Are they not pretending? Or do they not understand somehow differently, more clearly, than he the answers science gives to the questions that concerned him? And he diligently studied both the opinions of these people and the books that expressed these answers." - Tolstoy, "Anna Karenina"

"They do not covet truth, but victory and the dispelling of their own doubts. What they defend is some system, that is, some view about the totality of things, of which men are actually ignorant. No system would ever have been framed if people had been simply interested in knowing what is true, whatever it may be.” - George Santayana

“The old grey donkey stood by himself in a thistly corner of the Forest… and thought sadly to himself, “Why?” and sometimes he thought, “Wherefore?” and sometimes he thought, “Inasmuch as which?” and sometimes he didn’t quite know what he was thinking about.” — Eeyore